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 GBM

intersection of ideals for zero-dimensional schemes

 Syntax
 GBM(L: LIST): IDEAL

 Description
***** NOT YET IMPLEMENTED *****

This function computes the intersection of ideals corresponding to zero-dimensional schemes: GBM is for affine schemes, and HGBM for projective schemes. The list L must be a list of ideals. The function IntersectList should be used for computing the intersection of a collection of general ideals.

The name GBM comes from the name of the algorithm used: Generalized Buchberger-Moeller.

 Example
 /**/ Use P ::= QQ[x,y,z]; /**/ I1 := IdealOfPoints(P, mat([[1,2,1], [0,1,0]])); -- a simple affine scheme /**/ I2 := IdealOfPoints(P, mat([[1,1,1], [2,0,1]]))^2;-- another affine scheme ***** NOT YET IMPLEMENTED ***** GBM([I1, I2]); -- intersect the ideals ideal(xz + yz - z^2 - x - y + 1, z^3 - 2z^2 + z, yz^2 - 2yz - z^2 + y + 2z - 1, y^2z - y^2 - yz + y, xy^2 + y^3 - 2x^2 - 5xy - 5y^2 + 2z^2 + 8x + 10y - 4z - 6, x^2y - y^3 + 2x^2 + 2xy + 4y^2 - 3z^2 - 8x - 8y + 6z + 5, x^3 + y^3 - 7x^2 - 5xy - 4y^2 + 5z^2 + 16x + 10y - 10z - 7, y^4 - 2y^3 - 4x^2 - 8xy - 3y^2 + 4z^2 + 16x + 16y - 8z - 12) -------------------------------